If f is a function defined on ( 0 , 1 ) by f ( x ) = min x - [ x ] , - x - [ x ] , then ( f o f o f o f ) ( x ) is equal to ([.] greatest integer function)

Step-by-step solution

Given that, f is defined on 0 ,   1 by f ( x ) = min x - [ x ] , - x - [ x ] We know that Greatest Integer Function is a function that gives the greatest integer less than or equal to the number. If x ∈ 0 ,   1 , then x = 0 Also, for x ∈ 0 ,   1 , since x is positive, we have x > - x ⇒ f ( x ) = x Now, ( f o f o f o f ) ( x ) = ( f o f o f ) f ( x ) = ( f o f o f ) ( x ) = ( f o f ) f ( x ) = ( f o f ) ( x ) = f ( f ( x ) ) = x Hence, ( f o f o f o f ) ( x ) = x .